When the floods came, the unicorns were out frolicking and having fun -- they didn't want to get onto the ship -- and they realized their peril too late.

as the water rose, they used their magic in one last ditch effort to save themeves - but magic has a price -- they had to give up their beauty -- but they at least survived - and that is how we got these

Actually, some scientists have said they think the unicorn legend came from the Elasmotherium, which was basically a sort of rhino. Since the unicorn legend is so wide spread and since they don't know when the Elasmotherium became extinct they think that it might have existed in limited numbers as the same time as humans. Here's an artists drawing of what it might have looked like;